Can you have car finance in one name and register vehicle in another?

It's highly unlikely any finance company would agree to this. Just buy the vehicle, once its paid off, then you can sell or gift it to whomeoever you want.

Otherwise it would sound to the finance company like some kind of scam with misrepresentation from the start, possible grand theft auto and a defaulted finance note on a car that will quickly be totalled, disappear, or even worse an insurance fraud ring.

Another option if your trying to help a friend or family member is to offer to be a cosigner on the note, NOT a co-buyer, that is a totally different thing. If a car dealer says it is the same you need to exit the building right away because he is lying to you. a Co-signor is just guaranteeing payment on the financed note. A buyer or co-buyer is actually an owner and can be held jointly or separately financially liable for any all related injuries, accident claims traffic citations, violations, crimes, etc etc, that are ever associated with the vehicle throughout the time they are an owner whether actually driving the vehicle or not.

Answer

No. The owner of the vehicle is the guarantor of the loan.

As an owner you must register your car under your name.

You can have other cosigner, but basically you will be the primary responsible party.